1. A power cycle operates between a high temperature reservoir at temperature of 900°C and a low temperature reservoir at a temperature of 20°C. For steady state operation the heat transfer rate from the high temperature reservoir to the power cycle working fluid is 1000 kJ/min. Heat is rejected from the power cycle working fluid to the low temperature reservoir at the rate of 600 kJ/min.
(a) Calculate the thermal efficiency of the power cycle.
(b) Calculate the thermal efficiency for a reversible power cycle operating between the same low and high temperature reservoirs.
2. A refrigerator freezer compartment is maintained at a temperature of -15°F by removing heat at a rate of 4500 Btu/hr. The refrigerator is located in a room with a temperature of 75°F. The power input required to run the refrigerator is 1200 Btu/hr.
(a) Calculate the COP β for the refrigeration cycle.
(b) Calculate the rate of heat transfer (Btu/hr) from the refrigerant to the room.
(c) Calculate the power (Btu/hr) to run the cycle and the heat transfer rate (Btu/hr) from the refrigerant to the room if the refrigeration cycle was reversible. Assume that the heat transfer rate from the freezer compartment to the refrigerant is the same 4500 Btu/hr as for the actual cycle.
3. Six kilograms of CO2 executes at Carnot cycle in a piston-cylinder assembly. The minimum and maximum gas temperatures are 300 K and 900 K, respectively. The heat transfer to the CO2 during the isothermal expansion is 1200 kJ. At the end of the isothermal expansion the pressure is p3 = 800 kPa (assume that state 2 is the initial state of the isothermal expansion and state 3 is the final state of the isothermal expansion). After the adiabatic expansion from state 3 to state 4 the pressure is 14.73 kPa. Assume that CO2 is an ideal gas and use Table A-23 to evaluate the internal energy. For the Carnot cycle:
Process 1-2: Adiabatic compression to TH
Process 2-3: Isothermal expansion at TH, heat addition
Process 3-4: Adiabatic expansion to TC
Process 4-1: Isothermal compression at TC, heat rejection
(a) Determine the pressure (kPa) at states 1 and 2 and the volume (m3) of the gas at states 1-4.
(b) Determine the work (kJ) and heat transfer (kJ) for each process above.
(c) Sketch the process on a p-V diagram.
(d) Calculate the thermal efficiency based on the net work and the heat addition calculated above. Check to make sure that it matches the Carnot efficiency.
4. Ten kilograms of water initially at 200°C and 500 kPa undergoes an isothermal compressionprocess in a piston-cylinder system. At the end of the process, the water is a saturated liquid.
(a) Calculate the heat transfer (kJ) for the process.
(b) Calculate the work (kJ) for the process.